The magnifying power of a compound microscope can be increased by

Options

A. using both lenses of longer focal length
B. taking objective lens of shorter focal length
C. using both lenses of smaller focal length
D. taking objective lens of longer focal length and eye-lens of shorter focal length

Answer

To solve the question regarding how to increase the magnifying power of a compound microscope, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnifying Power**:
The magnifying power of a compound microscope is determined by the product of the magnification of the objective lens (MO) and the eyepiece (ME). Therefore, the formula is:
\[ \text{Total Magnification} = M_O \times M_E \]

2. **Relationship Between Magnification and Focal Length**:
The magnification of the objective lens (MO) is inversely proportional to its focal length (FO):
\[ M_O \propto \frac{1}{F_O} \]
Similarly, the magnification of the eyepiece (ME) is inversely proportional to its focal length (FE):
\[ M_E \propto \frac{1}{F_E} \]

3. **Increasing Magnification**:
To increase the magnification (both MO and ME), we need to reduce the focal lengths of both the objective lens and the eyepiece. This means:
- A smaller focal length results in higher magnification.

4. **Conclusion**:
Therefore, to increase the magnifying power of a compound microscope, we should use both lenses of smaller focal length. This will maximize the magnification from both the objective lens and the eyepiece.

### Final Answer:
The magnifying power of a compound microscope can be increased by using both lenses of smaller focal length.

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